Introduction

The interaction of a wave with a solid boundary leads to reflection, refraction, and diffraction. The water waves, like the light waves, may be reflected, refracted (turned or bent when they pass from one medium into another of different density) and diffracted (scattered in all directions when they impinge upon a barrier). The magnification of these phenomena depends on the shape and dimensions of the body (or bodies) impacted by the incident wave as well as on the motions of the barrier. As succinctly stated by Billingham and King (2000), the reflected/scattered/diffracted field is the difference between the unaffected incident wave and the actual solution.

The wave--body interaction is a complicated problem and cannot be solved without some simplifying assumptions. It is necessary to assume the fluid to be inviscid and incompressible, the flow to be unseparated, and the effects of surface tension, dissolved gases, cavitation, and vertical density and temperature gradients to be negligible. Then the flow field is represented by a scalar velocity potential, satisfying the Laplace equation within the fluid domain.

For a small body in ocean waves, D/L (the diffraction parameter) and the diffraction are negligibly small. For large bodies (with a typical volume ten times that of the great pyramid of Khufu), the relative fluid displacement UT/D and hence the viscous energy dissipation is small. Thus, the only source of energy dissipation is the propagation of the gravity waves, which undergo significant scattering or diffraction when the structure (devoid of sharp corners) spans more than about a fifth of the incident wavelength. This calls for a non-Morison type of analysis. In other words, the flow separation, coherence length, vortex shedding, wall roughness, wall turbulence, hydroelastic oscillations, and the Reynolds number become irrelevant or of negligible importance and the motion falls in the inertia-dominated regime.